Pentacircle chords: Difference between revisions

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A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 subgroup in the 11-odd-limit, tempering out the [[pentacircle comma]], 896/891. The pentacircle triads are three in number, 1-9/7-16/9 with steps 9/7-11/8-9/8; 1-9/7-16/11 with steps 9/7-9/8-11/8~~; and~~ 1-11/7-16/9 with steps 11/7-9/8-9/8. There are six pentacircle tetrads: the palindromic 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7; the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7; the inverse pair 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7~~; and~~ the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7. Finally, there are two pentacircle pentads, inversely related: 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8 ~~and~~ 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8.

A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 [[Just intonation subgroup|subgroup]] in the [[11-odd-limit]], [[tempering out]] the [[pentacircle comma]], [[896/891]].

The pentacircle [[Triad|triads]] are three in number:

* 1-9/7-16/9 with steps 9/7-11/8-9/8

* 1-9/7-16/11 with steps 9/7-9/8-11/8

* 1-11/7-16/9 with steps 11/7-9/8-9/8.

There are six pentacircle [[Tetrad|tetrads]]:

* the [[palindromic]] 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7

* the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7

* the [[inverse pair]] 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7

* the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7

Finally, there are two pentacircle [[Pentad|pentads]], inversely related:

* 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8

* 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8

The count of chords is triads: 3, tetrads: 6, pentads: 2, for a total of 11.

Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.

[[EDO|Equal divisions of the octave]] with pentacircle chords include [[22edo|22]], [[27edo|27]], [[41edo|41]], [[46edo|46]], [[58edo|58]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[121edo|121]], [[145edo|145]], [[167edo|167]], [[208edo|208]], [[266edo|266e]] and [[433edo|433bce]].

[[Category:11-odd-limit]]

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[[Category:Pentacircle]]

[[Category:Tetrad]]

~~[[Category:Todo:add links]]~~

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-A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 subgroup in the 11-odd-limit, tempering out the [[pentacircle comma]], 896/891. The pentacircle triads are three in number, 1-9/7-16/9 with steps 9/7-11/8-9/8; 1-9/7-16/11 with steps 9/7-9/8-11/8; and 1-11/7-16/9 with steps 11/7-9/8-9/8. There are six pentacircle tetrads: the palindromic 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7; the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7; the inverse pair 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7; and the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7. Finally, there are two pentacircle pentads, inversely related: 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8 and 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8.
+A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 [[Just intonation subgroup|subgroup]] in the [[11-odd-limit]], [[tempering out]] the [[pentacircle comma]], [[896/891]].
+The pentacircle [[Triad|triads]] are three in number:
+* 1-9/7-16/9 with steps 9/7-11/8-9/8
+* 1-9/7-16/11 with steps 9/7-9/8-11/8
+* 1-11/7-16/9 with steps 11/7-9/8-9/8.
+There are six pentacircle [[Tetrad|tetrads]]:
+* the [[palindromic]] 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7
+* the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7
+* the [[inverse pair]] 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7
+* the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7
+Finally, there are two pentacircle [[Pentad|pentads]], inversely related:
+* 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8
+* 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8
 The count of chords is triads: 3, tetrads: 6, pentads: 2, for a total of 11.
-Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.
+[[EDO|Equal divisions of the octave]] with pentacircle chords include [[22edo|22]], [[27edo|27]], [[41edo|41]], [[46edo|46]], [[58edo|58]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[121edo|121]], [[145edo|145]], [[167edo|167]], [[208edo|208]], [[266edo|266e]] and [[433edo|433bce]].
 [[Category:11-odd-limit]]
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 [[Category:Pentacircle]]
 [[Category:Tetrad]]
-[[Category:Todo:add links]]